Adjoint differential inclusions in necessary conditions for the minimal trajectories of differential inclusions

Necessary conditions of optimality for measure driven differential inclusions

Minimize h(x(0), x(1)) subject to dx(t) ∈ F (t, x(t))dt + G(t, x(t))dμ(t) ∀t∈[0, 1] (x(0), x(1)) ∈ C ⊂ IR × IR l(t, x(t)) ≤ 0 ∀t∈[0, 1] dμ ∈ K where h : IR × IR → IR, and l : [0, 1]× IR → IR are given functions, F : [0, 1]× IR → P(IRn), and G : [0, 1] × IR → P(IRn×q) are given set-valued maps, K ⊂ C∗([0, 1];K) is the set of control measures supported on [0, 1] with range in a given set K ⊂ IR, ...

Necessary and Sufficient Conditions for Viability for Semilinear Differential Inclusions

Given a set K in a Banach space X, we define: the tangent set, and the quasi-tangent set to K at ξ ∈ K, concepts more general than the one of tangent vector introduced by Bouligand (1930) and Severi (1931). Both notions prove very suitable in the study of viability problems referring to differential inclusions. Namely, we establish several new necessary, and even necessary and sufficient condit...

THE FULL AVERAGING OF FUZZY DIFFERENTIAL INCLUSIONS

In this paper the substantiation of the method of full averaging for fuzzy differential inclusions is considered. These results generalize the results of [17, 20] for differential inclusions with Hukuhara derivative and of [18] for fuzzy differential equations.

Improving the Solution of Fuzzy Differential Inclusions

Trajectories of Differential Inclusions with State Constraints

The paper deals with solutions of a differential inclusion ẋ ∈ F (x) constrained to a compact convex set Ω. Here F is a compact, possibly non-convex valued, Lipschitz continuous multifunction, whose convex closure coF satisfies a strict inward pointing condition at every boundary point x ∈ ∂Ω. Given a reference trajectory x∗(·) taking values in an ε-neighborhood of Ω, we prove the existence of ...